My experience is that the simple rfid readers are not able to discriminate amongst multiple tags read at once. If you bring 3 tags in range at once, you may be able to read one tag, but more likely will not read any tags at all. The tags are really dumb, and will all talk at once when they are placed in the reader's field and the reader is not super-great at discriminating the garbled tag info. Maybe addressable programmable tags could do it, I'm not sure.
I wonder if you could do what you want with those cheap SAW based radios. Have each ball peep out its identity at intervals and have a receiver near the bowl able to receive the signals of balls within -- say -- a metre.